Higher algebraic K-theory and tangent spaces to Chow groups

Identifier

etd-07082013-142038

Author

Sen Yang, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work, using higher algebraic K-theory, we provide an answer to the following question asked by Green-Griffiths in [13]: Can one define the Bloch-Gersten-Quillen sequence G_j on infinitesimal neighborhoods X_j so that Ker(G₁ &rarr G₀)= TG₀, Here TG₀ should be the Cousin resolution of TK_m(O_X) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of G_j is discussed in chapter 3, following [8] and [18]. The main theorems are theorem5.2.5, theorem 5.2.6 and theorem 5.2.8. The proof for the above theorems, given in chapter 5, requires non-trivial techniques from higher algebraic K-theory and negative cyclic homology. The main ingredients of the proof are: existence of Chern character at spectrum level, effacement theorem and Goodwillie-type and Cathelineau-type results.

Date

2013

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Yang, Sen, "Higher algebraic K-theory and tangent spaces to Chow groups" (2013). LSU Doctoral Dissertations. 2245.
https://repository.lsu.edu/gradschool_dissertations/2245

Committee Chair

Hoffman, Jerome

DOI

10.31390/gradschool_dissertations.2245